HULYAS Strict Solver

Auto-tunes β parameter iteratively until error ≤ 0.1% or max iterations. The 7-Step Wizard


Protocol ID	`zeq-solve-strict`
Category	ODE solver, master equation
Version	1.0
Endpoint	`/api/framework/solve/strict` 🔵 POST
Authentication	Required (Bearer API key)
Rate Limit	20/min

Purpose

Auto-tunes β parameter iteratively until error ≤ 0.1% or max iterations. The 7-Step Wizard It belongs to the ODE solver, master equation family and is callable as a single REST endpoint, a one-line SDK call, or via streaming where applicable.

What it does

When you call /api/framework/solve/strict, Zeq runs the HULYAS Strict Solver computation through the KO42 metric tensioner under the active HulyaPulse phase. The result is sealed at the next Zeqond boundary (0.777 s) and returned with a verifiable ZeqProof receipt — meaning the same inputs at the same phase always produce the same output, and any third party can later verify the result was computed at the time you claim.

In practice, this protocol takes the parameters listed below, performs its ode solver, master equation operation, and returns a structured response containing the computation output plus phase-locking metadata (zeqondTick, hulyaPhase, zeqProof).

When to use it

Reach for HULYAS Strict Solver when you need a ode solver, master equation primitive that:

Must be reproducible — every call is deterministic for a given phase
Must be auditable — every response carries a tamper-evident ZeqProof receipt
Must compose with other Zeq protocols — outputs are phase-aligned to 1.287 Hz so they slot directly into downstream calls without resync
Must scale across domains — the same endpoint works whether you're driving one call per minute or part of a high-throughput pipeline (subject to rate limit 20/min)

If you only need a one-shot ode solver, master equation answer with no audit trail and no composition with other Zeq calls, a plain library may be cheaper. If you need any of the four properties above, this protocol is the right tool.

How to call it

The fastest path is a single HTTPS POST request to /api/framework/solve/strict with a Bearer token. You can use cURL, JavaScript, Python, or any HTTP client — examples for all three are below. The response is JSON.

Parameters

Name	Type	Required	Description
`prompt`	`string`	Yes	Experiment description.
`koSettings`	`object`	No	Operator weights.
`maxIterations`	`number`	No	Max β-tuning iterations (1–20).

Returns

{ ...solverResult, betaFinal, tuneIterations, tuneStatus }

How to call it — every language

Every Zeq endpoint is a plain HTTPS POST. That means you can call it from any language that speaks HTTP. Below: thirteen working snippets — pick whichever fits your stack.

Command line (curl)

curl -X POST \
  https://www.zeq.dev/api/framework/solve/strict \
  -H "Authorization: Bearer $ZEQ_API_KEY" \
  -H "Content-Type: application/json" \
  -d '{
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
}'

JavaScript (browser / Node)

const res = await fetch("https://www.zeq.dev/api/framework/solve/strict", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.ZEQ_API_KEY}`,
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
}),
});
const data = await res.json();
console.log(data);

TypeScript

interface ZeqResponse<T = unknown> {
  ok: boolean;
  result: T;
  zeqondTick: number;
  hulyaPhase: number;
  zeqProof: string;
}

const res = await fetch("https://www.zeq.dev/api/framework/solve/strict", {
  method: "POST",
  headers: {
    "Authorization": `Bearer ${process.env.ZEQ_API_KEY}`,
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
}),
});
const data: ZeqResponse = await res.json();
console.log(data.result);

Python

import os, requests

res = requests.post(
    "https://www.zeq.dev/api/framework/solve/strict",
    headers={"Authorization": f"Bearer {os.environ['ZEQ_API_KEY']}"},
    json={
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
},
)
print(res.json())

Go

package main

import (
    "bytes"
    "encoding/json"
    "fmt"
    "io"
    "net/http"
    "os"
)

func main() {
    payload, _ := json.Marshal(map[string]interface{}{})
    req, _ := http.NewRequest("POST", "https://www.zeq.dev/api/framework/solve/strict", bytes.NewBuffer(payload))
    req.Header.Set("Authorization", "Bearer "+os.Getenv("ZEQ_API_KEY"))
    req.Header.Set("Content-Type", "application/json")
    res, _ := http.DefaultClient.Do(req)
    defer res.Body.Close()
    body, _ := io.ReadAll(res.Body)
    fmt.Println(string(body))
}

Java

import java.net.URI;
import java.net.http.HttpClient;
import java.net.http.HttpRequest;
import java.net.http.HttpResponse;

public class ZeqCall {
  public static void main(String[] args) throws Exception {
    HttpClient client = HttpClient.newHttpClient();
    HttpRequest req = HttpRequest.newBuilder()
        .uri(URI.create("https://www.zeq.dev/api/framework/solve/strict"))
        .header("Authorization", "Bearer " + System.getenv("ZEQ_API_KEY"))
        .header("Content-Type", "application/json")
        .POST(HttpRequest.BodyPublishers.ofString("{
  \"prompt\": \"<prompt>\",
  \"koSettings\": \"<koSettings>\",
  \"maxIterations\": 1
}"))
        .build();
    HttpResponse<String> res = client.send(req, HttpResponse.BodyHandlers.ofString());
    System.out.println(res.body());
  }
}

C

#include <stdio.h>
#include <stdlib.h>
#include <curl/curl.h>

int main(void) {
    CURL *curl = curl_easy_init();
    if (!curl) return 1;
    struct curl_slist *headers = NULL;
    char auth[256];
    snprintf(auth, sizeof(auth), "Authorization: Bearer %s", getenv("ZEQ_API_KEY"));
    headers = curl_slist_append(headers, auth);
    headers = curl_slist_append(headers, "Content-Type: application/json");
    curl_easy_setopt(curl, CURLOPT_URL, "https://www.zeq.dev/api/framework/solve/strict");
    curl_easy_setopt(curl, CURLOPT_CUSTOMREQUEST, "POST");
    curl_easy_setopt(curl, CURLOPT_HTTPHEADER, headers);
    curl_easy_setopt(curl, CURLOPT_POSTFIELDS, "{
  \"prompt\": \"<prompt>\",
  \"koSettings\": \"<koSettings>\",
  \"maxIterations\": 1
}");
    curl_easy_perform(curl);
    curl_slist_free_all(headers);
    curl_easy_cleanup(curl);
    return 0;
}

C++

#include <iostream>
#include <cstdlib>
#include <curl/curl.h>

int main() {
    CURL* curl = curl_easy_init();
    if (!curl) return 1;
    struct curl_slist* headers = nullptr;
    std::string auth = "Authorization: Bearer ";
    auth += std::getenv("ZEQ_API_KEY");
    headers = curl_slist_append(headers, auth.c_str());
    headers = curl_slist_append(headers, "Content-Type: application/json");
    curl_easy_setopt(curl, CURLOPT_URL, "https://www.zeq.dev/api/framework/solve/strict");
    curl_easy_setopt(curl, CURLOPT_CUSTOMREQUEST, "POST");
    curl_easy_setopt(curl, CURLOPT_HTTPHEADER, headers);
    curl_easy_setopt(curl, CURLOPT_POSTFIELDS, R"json({
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
})json");
    curl_easy_perform(curl);
    curl_slist_free_all(headers);
    curl_easy_cleanup(curl);
}

PHP

<?php
$ch = curl_init("https://www.zeq.dev/api/framework/solve/strict");
curl_setopt($ch, CURLOPT_CUSTOMREQUEST, "POST");
curl_setopt($ch, CURLOPT_HTTPHEADER, [
    "Authorization: Bearer " . getenv("ZEQ_API_KEY"),
    "Content-Type: application/json",
]);
curl_setopt($ch, CURLOPT_POSTFIELDS, '{
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
}');
curl_setopt($ch, CURLOPT_RETURNTRANSFER, true);
$response = curl_exec($ch);
curl_close($ch);
echo $response;

Swift

import Foundation

var req = URLRequest(url: URL(string: "https://www.zeq.dev/api/framework/solve/strict")!)
req.httpMethod = "POST"
req.setValue("Bearer \(ProcessInfo.processInfo.environment["ZEQ_API_KEY"] ?? "")", forHTTPHeaderField: "Authorization")
req.setValue("application/json", forHTTPHeaderField: "Content-Type")
req.httpBody = "{
  \"prompt\": \"<prompt>\",
  \"koSettings\": \"<koSettings>\",
  \"maxIterations\": 1
}".data(using: .utf8)

URLSession.shared.dataTask(with: req) { data, _, _ in
    if let data = data { print(String(data: data, encoding: .utf8) ?? "") }
}.resume()

Lua

local http = require("socket.http")
local ltn12 = require("ltn12")
local response = {}

http.request{
    url = "https://www.zeq.dev/api/framework/solve/strict",
    method = "POST",
    headers = {
        ["Authorization"] = "Bearer " .. os.getenv("ZEQ_API_KEY"),
        ["Content-Type"] = "application/json",
        ["Content-Length"] = tostring(#'{
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
}'),
    },
    source = ltn12.source.string('{
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
}'),
    sink = ltn12.sink.table(response),
}
print(table.concat(response))

HTML (drop into any page)

<script>
fetch("https://www.zeq.dev/api/framework/solve/strict", {
  method: "POST",
  headers: {
    "Authorization": "Bearer YOUR_ZEQ_API_KEY",
    "Content-Type": "application/json",
  },
  body: JSON.stringify({
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
}),
})
  .then(r => r.json())
  .then(data => console.log(data));
</script>

Markdown / REST Client (.http)

POST https://www.zeq.dev/api/framework/solve/strict
Authorization: Bearer {{ZEQ_API_KEY}}
Content-Type: application/json

{
  "prompt": "<prompt>",
  "koSettings": "<koSettings>",
  "maxIterations": 1
}

Phase-Locking & ZeqProof

Every response from /api/framework/solve/strict carries:

zeqondTick — the Zeqond (0.777 s) at which the result was sealed
hulyaPhase — the HulyaPulse phase ∈ [0, 1) at sealing
zeqProof — HMAC receipt that lets any third party verify the result without an API key via POST /api/zeq/prove/verify

See Concepts → ZeqProof and HulyaPulse for the underlying mathematics.

All protocols in this family — see the ODE solver, master equation category
API Reference → Endpoints
Concepts → ZeqProof

Purpose​

What it does​

When to use it​

How to call it​

Parameters​

Returns​

How to call it — every language​

Command line (curl)​

JavaScript (browser / Node)​

TypeScript​

Python​

Go​

Java​

C​

C++​

PHP​

Swift​

Lua​

HTML (drop into any page)​

Markdown / REST Client (.http)​

Phase-Locking & ZeqProof​

Related​